Godbillon-Vey序列与Francoise算法
Godbillon-Vey sequence and Francoise algorithm
摘要：
我们认为叶理给出的变形$dF+εω$的确切形式$dF$在$\mathbb{C}^2$在一个社区的一个家庭的周期$γ(t)\subset F^{-1}(t)$。1996年Francoise给出了一种算法，用于计算沿这种变形的$γ$的位移函数$Δ$的第一个非零项。该算法使人想起1971年为研究$ω$的可积性而发现的著名的Godbillon-Vey序列。在本文中，我们建立了这两种方法之间的对应关系，并将Casale的一些结果与有限Godbillon-Vey序列的可积性类型相关到Francoise算法设置。
英文摘要：
We consider foliations given by deformations $dF+εω$ of exact forms $dF$ in $\mathbb{C}^2$ in a neighborhood of a family of cycles $γ(t)\subset F^{-1}(t)$. In 1996 Francoise gave an algorithm for calculating the first nonzero term of the displacement function $Δ$ along $γ$ of such deformations. This algorithm recalls the well-known Godbillon-Vey sequences discovered in 1971 for investigation integrability of a form $ω$. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability for finite Godbillon-Vey sequences to the Francoise algorithm settings.
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